一维反应扩散方程中的行波波速及行波解

基金项目: 国家自然科学基金资助项目(19901034)

Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension

Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P R China

摘要: 通过Painlev啨分析,详细研究了一类一维化学反应扩散方程中的行波解及波速。分别给出了当歼灭项的指数大于创造项的指数及创造项的指数大于歼灭项的指数时,这两种情形下的波速及行波解的显式表示。此外,还给出了一类常见激励介质中的波速及平面波解在薄的边界层内的公式。
- Painlev啨分析 /
- 行波 /
- 激励介质
Abstract: By Painlev analysis,traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated.When the exponent of the creation term is larger than the one of the annihilation term,two typical cases are studied, one with the exact traveling wave solutions,yielding the values of speeds,the other with the series expansion solution,also yielding the value of speed.Conversely,when the exponent of creation term is smaller than the one of the annihilation term,two typical cases are also studied,but only for one of them,there is a series development solution,yielding the value of speed,and for the other,traveling wave solution cannot exist.Besides,the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.
- Painlev analysis /
- traveling wave /
- excitable media

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